An Arbitrary Order Virtual Element Method for Free Torsional Vibrations of Beams

In this study, a novel arbitrary order Virtual Element Method (p-VEM) for free torsional vibration analysis of beams with negligible warping is presented. This method can serve as an equivalent beam model for slender aerospace structural components. The proposed formulation utilizes a spatial discretization of the primary variable with implicit virtual functions that are approximated with polynomials of arbitrary order p by employing a suitably defined projection operator and degrees of freedom. From the spatial discretization of the weak form of the equations of motion, the semi-discrete equations of motion are obtained, from which stiffness and mass matrices are derived without the need for additional stabilization. The developed formulation is validated through several case studies, which demonstrate that the p-VEM offers higher accuracy and faster convergence rate compared to traditional modeling approaches.